Although pulse oximeters have been used extensively over the last few years in all major hospitals, the theoretical basis of pulse oximetry is still poorly understood. As a result, the development of instrumentation has relied on the slow acquisition of empirical knowledge. Recently, clinicians have expressed interest in the possibility of developing a transcutaneous oximeter that operates in the reflection mode, rather than in the transmission mode. Such a device could be used at many sites on the body, and may enable monitoring during shock and other conditions during which peripheral blood flow is compromised. Our efforts have been focused on improving the theoretical understanding of pulse oximetry. We have developed photon-diffusion models of the skin to study the effect of tissue blood volume and other important variables on the calibration of transmission - and reflection-mode oximeters. Measurements on tissue phantoms and intact skin have been made to confirm the validity of the models. Guided by the model results, we have constructed solid-state reflectance sensors which can be placed on the forehead, face, and chest to obtain measurements of arterial oxygen saturation.